Pith Number

pith:ZKOBKUQV

pith:2015:ZKOBKUQVUDA6TWWPXG42U7FIE2

not attested not anchored not stored refs pending

Spectral dimension and Bohr's formula for Schrodinger operators on unbounded fractal spaces

Alexander Teplyaev, Joe P. Chen, Stanislav Molchanov

arxiv:1505.03923 v2 · 2015-05-14 · math-ph · math.FA · math.MG · math.MP · math.PR · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZKOBKUQVUDA6TWWPXG42U7FIE2}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:33:58.338010Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca9c155215a0c1e9dacfb9b9aa7ca826bc7221f41905c6664e0e18c67ae58d72

Aliases

arxiv: 1505.03923 · arxiv_version: 1505.03923v2 · doi: 10.48550/arxiv.1505.03923 · pith_short_12: ZKOBKUQVUDA6 · pith_short_16: ZKOBKUQVUDA6TWWP · pith_short_8: ZKOBKUQV

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZKOBKUQVUDA6TWWPXG42U7FIE2 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ca9c155215a0c1e9dacfb9b9aa7ca826bc7221f41905c6664e0e18c67ae58d72

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e23688bce1c3bcd287917a2bab8a75ea11d48c8d8974a5ed7b4eb27cb2eea092",
    "cross_cats_sorted": [
      "math.FA",
      "math.MG",
      "math.MP",
      "math.PR",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-05-14T23:56:41Z",
    "title_canon_sha256": "89ddc5e6cf87eb05ccd5cff63fac5b142342cf2adcef558d6fb6d00cec7acaa1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.03923",
    "kind": "arxiv",
    "version": 2
  }
}